Answer:
Just like combining like terms with the same variables, you combine like
radicals with the same number under the radical signs.
Step-by-step explanation:
Example:
3x + 2x
= 5x {combined like terms}
3√2 + 2√2
= 5√2 {combined like radicals}
Combining two or more terms are similar to combining two or more radicals.
What is a radical?
The 'n' th root of a number 'x' is written as [tex]\sqrt[n]{x}[/tex]. It is called a radical.
Combining two or more terms:
(a + 2a + 97a) = 100a
Combining two or more radicals:
(a[tex]\sqrt{3}[/tex] + 9a[tex]\sqrt{3}[/tex] + 90a[tex]\sqrt{3}[/tex]) = 100a[tex]\sqrt{3}[/tex]
Therefore, combining two or more terms are similar to combining two or more radicals.
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A wheelchair ramp is 8.0 m long. The angle of inclination is 10°. Calculate the rise of
the ramp to the nearest tenth of a meter.
Answer:
The height of the ramp is 1.39 m.
Step-by-step explanation:
We have,
A wheelchair ramp is 8.0 m long
The angle of inclination is 10°
It is required to find the rise of the ramp.
Here, hypotenuse is 8 m and angle of inclination is 10°.
Using trigonometry to find it.
[tex]\sin\theta=\dfrac{x}{8}[/tex]
x is rise of the ramp
[tex]x=\sin(8)\times 10\\\\x=1.39\ m[/tex]
So, the height of the ramp is 1.39 m.
Please hurry
What function is represented in the table?
Answer:
B. 3(2^x)
Step-by-step explanation:
3(2^x) is the only function that yielded the given outputs when the inputs were plugged in.
Which statement about the figures shown below is true?
PLS HEP ASP BEST GETS FOLLOW AND BRAINLIEST
Danville Street and Belmont Avenue intersect. If the diagonal distance across the intersection is 9.6 meters and Danville Street is 8.1 meters wide, how wide is Belmont Avenue? If necessary, round to the nearest tenth.
Answer:
Width of Belmont Avenue is 5.2 meters
Step-by-step explanation:
We use the Pythagoras theorem to solve the problem
Pythagoras Theorem states that:
Hypotenuse² = Base² + Perpendicular²
Danville Street, Belmont Avenue and their diagonal forms a right angled triangle
In this case, let the base be Danville Street with width of 8.1 meters
Let the hypotenuse be 9.6 meters
We need to find the perpendicular
Put the values in Pythagoras theorem.
9.6² = 8.1² + perpendicular²
perpendicular² = 9.6²-8.1²
perpendicular² = 92.16 - 65.61
perpendicular² = 26.55
take square root on both sides
perpendicular =5.153
Round of to nearest 10th
Perpendicular = 5.2 meters
Belmont Avenue = 5.2 meters
A pizza shop charges customers based on the area of the pizza they order. The cost of a pizza in dollars can be represented by
S(r) - 0.12. where r is the radius of the pizza in inches.
What is the diameter of a pizza that costs $26.327 Round to the nearest hundredth.
Answer:
$26.300
Step-by-step explanation:
well if its 5 or more u round to the next whole number but if its 5 or under you just round whatever ur rounding into the same number but whole
Giving brainliest, please answer as soon as possible.
Answer:
Step-by-step explanation:
There are five lines of symmetry in a regular pentagon:
Each going from side midpoint to opposite vertex.
here is a drawing of all of them filled in:
what graph best shows a positive correlation between the number of hours studied and the test scores ?
I just need the bottom question plz I need it for today
Answer:
i dunno i just want points xd so i can put questions xd
Step-by-step explanation:
Answer:
The angles are 31 and 59 degrees.
Step-by-step explanation:
Let x be angle. Let 90-x be the complement of its angle. Then, x=90-x+28 since the measure of an angle is 28 degrees more than the complement.
Solving equation in Step 3 yields the following steps Add x to both sides of the equation Divide by 2 to both sides of the equation
There are 7 red cards and 13 blue cards
in a deck of cards. If Yuki randomly
selects a card from the deck, what is the
probability that it is a red card?
Answer:
7/20
Step-by-step explanation:
#red cards/total # of cards
7/(7+13)
7/20
Answer:
7/20
Step-by-step explanation:
Please help me I need to submit this asap
Answer:
D
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here { a, b ] = [ - 1, 2 ], thus
f(b) = 4 ← from (2, 4 )
f(a) = [tex]\frac{1}{2}[/tex] ← from (- 1, [tex]\frac{1}{2}[/tex] ) , thus
average rate of change = [tex]\frac{4-\frac{1}{2} }{2-(-1)}[/tex] = [tex]\frac{\frac{7}{2} }{3}[/tex] = [tex]\frac{7}{6}[/tex] → D
Tammy has $3,500 that she wants to invest in stock. She believes she can earn a 12% annual return. What would be the value of Tammy's investment in 10 years if she is able to achieve her goal?
Answer:
the answer to the following questions is 10870.46873
Explain in words how to use the side lengths of a triangle to determine if the triangle is a right, acute, or obtuse triangle.
basically write the triangle in degree language like this is a acute angle because this is a 70* degree angle and talk more
Tommy can exchange 8 euros for 11 dollars.At this rate, how many dollars can Tommy get with 12 euros?
Answer:
16.50 dollars
Step-by-step explanation:
We can use proportion
8 euros --- 11 dollars
12 euros --- x dollars
x = 12 * 11/8 = 16.5= 16.50 dollars
Answer:
16.5 dollars
Step-by-step explanation:
Let's make a proportion using the following setup.
dollars/euros=dollars/euros
Tommy can get 11 dollars for 8 euros. We don't know how many dollars he can get with 12 euros. Therefore, we can say that he can get x dollars with 12 euros.
11 dollars/8 euros=x dollars/12 euros
11/8=x/12
We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
x is being divided by 12. The opposite of division is multiplication. Multiply both sides by 12.
12*(11/8)=(x/12)*12
12*11/8=x
12*1.375=x
16.5=x
Tommy can get $16.50 with 12 euros.
k(-1) =
PLEASE HELP ASAP
Answer:
7?
Step-by-step explanation:
Answer:
k(-1) = 7
Step-by-step explanation:
the blue line represents the graph of k. The question is asking what the y-value at x=-1 is. Therefore, you just look at the blue line when x = -1, which is one block to the left of the middle. At that point, the y value is 7.
On a map, 1 inch equals 9.4 miles. Two houses are 1.5 inches apart on the map. What is the actual distance between the houses? Use pencil and paper. Show how you can represent the scale with two different ratios. What ratio is more helpful for solving the problem? Explain.
Answer:
14.1 I think
Step-by-step explanation:
Answer:14.1
Step-by-step explanation:
Evaluate when a=-6, b= 5, C= -2:
a3 - b + 402
f
Select one:
stion
a. 109
O b. 205
O c. 81
O d. -205
Answer:
c 81
Step-by-step explanation:
Kristin spent $128 on shirts. Fancy shirts cost $20 and plain shirts cost $10. If she bought a total of 8
shirts, then how many of each kind did she buy?
Answer:
6 Fancy shirts
Step-by-step explanation:
Determine whether the triangles are similar. If so, write a similarity statement. answers:: A) The triangles are similar; ΔQRS ∼ ΔTUV. B) There isn't enough information to determine whether the triangles are similar. C) The triangles are not similar. D) The triangles are similar; ΔQRS ∼ ΔVUT.
Answer:
C) The triangles are not similar
Step-by-step explanation:
There are 3 triangle similarity theorems:
If two of the angles are the same, the third angle is the same and the triangles are similar.If the three sides are in the same proportions, the triangles are similar.If two sides are in the same proportions and the included angle is the same, the triangles are similar.We can find the all the angles of both triangles, so we can determine the similarity of these triangles only by first theorem
Angles of ΔQRS:
<Q = 63°
<R = 90°
<S = 180°-63°-90° = 27°
Angles of ΔTUV:
<T=180°-90°-25° = 65°
<U = 90°
<V = 25°
As none of the angles are same, triangles are not similar.
The parent function f(x) = 5 ^ x has been venically compressed by a factor of one-half shifted to the three units and up two units choose the correct function
Answer:
See the explanation
Step-by-step explanation:
The given function is:
f(x) = 5ˣ
Transformation of a parent function is given by the formula:
g(x) = k · f(x + a) + b
Where
k represents vertical compression if |k| < 1 and k represents vertical stretch of |k| > 1
f(x) shifts left by a units if a>0 and f(x) shift right by a units if a<0
f(x) shift up by b units if b>0 and f(x) shifts down by b units if b<0
In the question it is given:
k = 1/2
Shifts right by 3 units ⇒ a = -3
Shift up by 2 units ⇒ b = 2
Substitute in the formula:
g(x) = (1/2) · f(x - 3) + 2
[tex]g(x) = \frac{1}{2}\cdot5^{x-3}+2[/tex]
A sequence is defined by the recursive formula f(n+) = f(n) -2. If f(1) =18 what is f(5)?
=====================================================
Work Shown:
Plug in n = 1 to find the next term
f(n+1) = f(n) - 2
f(1+1) = f(1) - 2 ... replace every n with 1
f(2) = f(1) - 2
f(2) = 18-2 .... replace f(1) with 18
f(2) = 16
We'll use this to get the next term. Plug in n = 2
f(n+1) = f(n) - 2
f(2+1) = f(2) - 2 ... replace every n with 2
f(3) = f(2) - 2
f(3) = 16 - 2 ... replace f(2) with 16
f(3) = 14
This process keeps going until we reach f(5)
Plug in n = 3
f(n+1) = f(n) - 2
f(3+1) = f(3) - 2
f(4) = f(3) - 2
f(4) = 14-2
f(4) = 12
and finally plug in n = 4
f(n+1) = f(n) - 2
f(4+1) = f(4) - 2
f(5) = f(4) - 2
f(5) = 12 - 2
f(5) = 10
The summary is basically we subtract 2 from each term to get the next term. The sequence is 18, 16, 14, 12, 10 which is arithmetic.
Click on the median in this set of data. 15,21,25,63,8
Answer:
the median is 21
Step-by-step explanation:
8 , 15 , 21 , 25 , 63
that is what you have to do you would have to put them in order from least to greatest so then you would see the middle number which is 21
The line has a slope of 7/10 and a y intercept of 3/10. Find the equation of the line.
Answer:
y=7/10+3/10
Step-by-step explanation:
Marc had $7.50. He bought toy car for $6.49 how much money does Marc have left
Answer:
7.50 - 6.49 = $1.01 left
Answer:
1.01
Step-by-step explanation:
7.50 - 6.49 = 1.01
If the relationship below are given in form (input, output), Which pairing always describes a function?
Answer:
Step-by-step explanation:
i'm not sure what the answer options are since they're not provided, but it's whichever option has a steady rate of change. (ex: money, time spent earning it; location, time spent driving; length in inches, length in meters)
In the diagram below, points A and B represent two lakes. How far apart are the lakes? 131.5 ft 456.3 ft 474.6 ft 633.9 ft
Answer:
I don't know the answer, but I just took a test and the answers ARE NOT 456.3 and ARE ALSO NOT 474.6
Step-by-step explanation:
The distance between the two lakes = 633.9 ft. So, we take the 4th option.
What is the law of cosines?By the law of cosines, a triangle with sides a, b, and c, and the angle opposite to c being γ,
c = √(a² + b² - 2.a.b.cos γ)
How do we solve the given question?To solve the question, we will use the law of cosines.
Let a = 560 ft., b = 350 ft., c = d (unknown distance).
γ = 160° - 75° = 85°.
We substitute the values in the formula to get,
d = √(560² + 350² - 2(560)(350)(cos 85°)
or, d = √(313600 + 122500 - 392000*0.0871)
or, d = √(436100 - 34165.05116)
or, d = √401934.948842
or, d = 633.983397
So, we take d = 633.9 ft., the 4th option.
∴ The distance between the two lakes = 633.9 ft.
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Please help!!!!! WILL MARK BRAINLIEST!!!!
Graph the system of linear inequalities on the coordinate plane y>/-1/2x+2 1/2
Y<1/5x+6
A) shade the solution to the system of inequalities
B) pick a point and show your solution is correct
Answer:
see below
Step-by-step explanation:
y[tex]\geq[/tex] ..... means full line and shading above the line
Y< ......means doted line and shading below the line
A) solution is overlapping shaded part
B) (10,5)
plug in point in inequalities and check if it's true; if it's true you showed that solution is correct
1. 5[tex]\geq[/tex]-1/2*10 + 2 1/2
5[tex]\geq[/tex] -5 + 2 1/2
5[tex]\geq[/tex] -2 1/2 TRUE
2. 5[tex]<[/tex]1/5*10 + 6
5< 2 + 6
5< 8 TRUE
The solution to the inequality equation is ( -5 , 5 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the first inequality relation be represented as A
Now , the value of A is
y ≥ ( -1/2 )x + 2 1/2
y ≥ ( -1/2 )x + 5/2 be equation (1)
Let the second inequality relation be represented as B
Now , the value of B is
y < ( 1/5 )x + 6
On simplifying the equation , we get
Graphing the inequalities we get the common point as ( -5 , 5 )
Substitute the value of x = -5 and y = 5 in the inequality equations , we get
y ≥ ( -1/2 )x + 5/2
Substitute x = -5 and y = 5
5 ≥ ( -1/2 ) ( -5 ) + 5/2
5 ≥ 5/2 + 5/2
5 ≥ 10/2
5 ≥ 5
The inequality is true
Now , y < ( 1/5 )x + 6
Substitute x = -5 and y = 5
5 < ( 1/5 ) ( -5 ) + 6
5 < -1 + 6
5 < 5
The inequality is true when the value of x > -5
Hence , the equations are solved
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HELP!!! Please , solve this
Answer:
Equivalent
Step-by-step explanation:
15/25 and 3/5 are equivalent hope this helps
Answer:
I also think it's equivalent because it has a equal sign but I'm dumb so don't trust my answer.
Step-by-step explanation:
What is the value of log6255?
Answer:
1/4
Brainliest!Step-by-step explanation:
1/4 on my calculator
The value of log 5 to the base 625 is 1/4 .
How to find the value of logarithm with any base value -From the definition of logarithm , we know that if log a to the base b is equal to x , where a, b are non negative integer and x is an assumed positive integer then we have ,
∴ log a to the base b = x
⇒ [tex]a = b^{x}[/tex]
Thus we can take log 5 to the base 625 = x
∴ [tex]5 = 625^{x}[/tex]
From the above equation, we can get the value of x as 1/4
Thus the value of log 5 to the base 625 is 1/4
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12. Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welcome to stay, but she charges $10 per person. She expects guests to check out by 10 a.m. and charges an extra $5 per hour for late checkouts. Select the linear equation that correctly represents how much Martina collects for one night of stay in her home.
A) c = 25 + 10p + 5h
B) c = 25 – 10p – 5h
C) c + 25 = 10p + 5h
D) c = 25 + 10 + 5
Answer:
Step-by-step explanation:
the answer is A
BECAUSE the fixed charged or the charged that is always there is 25 dollars plus and additional cost for 10 dollars per person plus additional cost depending on how many hours u stay past 10 am
(30 points)PLEASE HELP! LOVE Y'ALL SO MUCH THX! If x=3b and y= 2/6b+4 , what is y in terms of x?
(A) 2 x+4 (B) 1 x+2 (C) 2x (D) x+2 (E) 2x+4
Answer:
y=(1/9)x+4
Step-by-step explanation:
x=3b
b=(1/3)x
y=2/6(1/3)x+4
y=(2/18)x+4
y=(1/9)x+4
Answer:
y = 1/(x+2)
Step-by-step explanation:
x=3b and y= 2/(6b+4)
Rewriting the second equation by factoring out 2
y=2/ 2(3b+2)
We know that 3b = x
y=2/ 2(x+2)
Canceling the 2 in the numerator and denominator
y = 1/(x+2)